Applied Mathematics Letters最新文献

{"title":"A generalized Nyström method with subspace iteration for low-rank approximations of large-scale nonsymmetric matrices","authors":"Yatian Wang ,&nbsp;Nian-Ci Wu ,&nbsp;Yuqiu Liu ,&nbsp;Hua Xiang","doi":"10.1016/j.aml.2025.109531","DOIUrl":"10.1016/j.aml.2025.109531","url":null,"abstract":"<div><div>In numerical linear algebra, finding the low-rank approximation of large-scale nonsymmetric matrices is a core problem. In this work, we combine the generalized Nyström method and randomized subspace iteration to propose a new low-rank approximation algorithm, which we refer to as the generalized Nyström method with subspace iteration. Moreover, utilizing the projection theory, we perform an in-depth error analysis from a novel perspective and establish the theoretical error bound of the proposed algorithm. Finally, numerical experiments show that our method outperforms the randomized singular value decomposition and generalized Nyström method in accuracy, especially when applied to a matrix with slowly decaying singular values.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109531"},"PeriodicalIF":2.9,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143551292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quasi-exponential stability of non-autonomous integro-differential systems with infinite delay","authors":"Liguang Xu ,&nbsp;Hongxiao Hu","doi":"10.1016/j.aml.2025.109520","DOIUrl":"10.1016/j.aml.2025.109520","url":null,"abstract":"<div><div>The current article focuses on the quasi-exponential stability analysis of non-autonomous integro-differential systems characterized by infinite delay. By developing a novel generalized Halanay inequality, sufficient conditions for the quasi-exponential stability of non-autonomous integro-differential systems with infinite delay are presented for the systems.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109520"},"PeriodicalIF":2.9,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143526859","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On bounds for norms and conditioning of Wasserstein metric matrix","authors":"Zhong-Zhi Bai","doi":"10.1016/j.aml.2025.109510","DOIUrl":"10.1016/j.aml.2025.109510","url":null,"abstract":"<div><div>For the Wasserstein-1 metric matrices of one- and two-dimensions, we prove the two guesses about their computational properties, which were proposed by Bai in 2024 (Linear Algebra Appl. 681(2024), 150-186). More specifically, for these matrices we prove their nonsingularity and symmetric positive definiteness, and derive sharper upper bounds on the norms of their inverses and on their condition numbers, under much more relaxed and realistic conditions imposed upon the involved problem and discretization parameters.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109510"},"PeriodicalIF":2.9,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143551293","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Bistable traveling waves of a nonlocal reaction–diffusion model with non-monotone birth pulse","authors":"Binxiang Dai,&nbsp;Yaobin Tang","doi":"10.1016/j.aml.2025.109519","DOIUrl":"10.1016/j.aml.2025.109519","url":null,"abstract":"<div><div>This paper considers a nonlocal reaction–diffusion model with a non-monotone birth pulse and a bistable response term. We define two monotone semiflows and, using the comparison argument, obtain the threshold dynamics between persistence and extinction in bounded domain. Moreover, we apply the asymptotic fixed point theorem to show the existence of bistable traveling wave solutions.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109519"},"PeriodicalIF":2.9,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143520749","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"About stability of a mathematical model of Glassy-winged Sharpshooter population under Poisson’s jumps","authors":"Leonid Shaikhet","doi":"10.1016/j.aml.2025.109523","DOIUrl":"10.1016/j.aml.2025.109523","url":null,"abstract":"<div><div>The known mathematical model of Glassy-winged Sharpshooter, described by a nonlinear differential equation with delay, is considered under a combination of stochastic perturbations of the type of white noise and Poisson’s jumps. It is assumed that stochastic perturbations are directly proportional to the deviation of the system state from the positive equilibrium. Via the general method of Lyapunov functionals construction two different conditions for stability in probability of the model equilibrium are obtained. Numerical simulations and figures illustrate the obtained results.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109523"},"PeriodicalIF":2.9,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143535240","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Uniqueness of weak solutions to one-dimensional doubly degenerate cross-diffusion system","authors":"Xiuqing Chen,&nbsp;Bang Du","doi":"10.1016/j.aml.2025.109521","DOIUrl":"10.1016/j.aml.2025.109521","url":null,"abstract":"<div><div>The uniqueness of global weak solutions to one-dimensional doubly degenerate cross-diffusion system is shown. The equations model the evolution of feeding bacterial populations in a malnourished environment. The key idea of the proof is applying anti-derivative of the sum of weak solutions to the system.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109521"},"PeriodicalIF":2.9,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143529760","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Sharp-interface limit of the Cahn–Hilliard–Biot equations","authors":"Erlend Storvik,&nbsp;Carina Bringedal","doi":"10.1016/j.aml.2025.109522","DOIUrl":"10.1016/j.aml.2025.109522","url":null,"abstract":"<div><div>In this letter, we derive the sharp-interface limit of the Cahn–Hilliard–Biot equations using formal matched asymptotic expansions. We find that in each sub-domain, the quasi-static Biot equations are obtained with domain-specific material parameters. Moreover, across the interface, material displacement and pore pressure are continuous, while volumetric fluid content and normal stress are balanced. By utilizing the energy of the system, the phase-field potential is shown to be influenced by the curvature, along with contributions from both flow and elasticity at the interface. The normal velocity of the interface is proportional to the jump in normal derivative of the phase-field potential across the interface. Finally, we present a numerical experiment that demonstrates how the location of each phase evolves consistently as the diffuse-interface width parameter becomes smaller; only the width of the diffuse interface changes.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109522"},"PeriodicalIF":2.9,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143526860","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamics of non-local lattice systems in ℓ1","authors":"Jiaohui Xu ,&nbsp;Tomás Caraballo ,&nbsp;José Valero","doi":"10.1016/j.aml.2025.109509","DOIUrl":"10.1016/j.aml.2025.109509","url":null,"abstract":"<div><div>In this paper, the well-posedness and asymptotic behavior of a non-local lattice system are analyzed in the space <span><math><msup><mrow><mi>ℓ</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>. In fact, the analysis is carried out in the subspace <span><math><msubsup><mrow><mi>ℓ</mi></mrow><mrow><mo>+</mo></mrow><mrow><mn>1</mn></mrow></msubsup></math></span> formed by the nonnegative elements, remaining open the case of the whole space. The same problem has been analyzed recently in the space <span><math><msup><mrow><mi>ℓ</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> (see Y. Li et al., Communications on Pure and Applied Analysis, 23 (2024), 935-960). However, the latter does not allow us to consider non-local terms which are natural in the modeling of reaction–diffusion problems introduced by M. Chipot in the wide literature published on this problem. With the current analysis, it is possible to investigate these interesting situations.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"165 ","pages":"Article 109509"},"PeriodicalIF":2.9,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143510544","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Localized radial basis function collocation method for long-time simulation of nonlinear transient heat conduction problems","authors":"Yikun Wang ,&nbsp;Xiaohan Jing ,&nbsp;Lin Qiu","doi":"10.1016/j.aml.2025.109525","DOIUrl":"10.1016/j.aml.2025.109525","url":null,"abstract":"<div><div>This paper introduces a hybrid numerical method for simulating two- and three-dimensional nonlinear transient heat conduction problems with temperature-dependent thermal conductivity over extended time intervals. The approach employs the Krylov deferred correction method for temporal discretization, which is particularly effective for dynamic simulations requiring high accuracy. After temporal discretization, the resulting nonlinear equation is solved in the spatial domain using the localized radial basis function collocation method, with its performance further improved by incorporating a newly developed radial basis function. Numerical experiments on two test cases validate the effectiveness and stability of the proposed hybrid method.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"165 ","pages":"Article 109525"},"PeriodicalIF":2.9,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143519811","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global solvability in a singular chemotaxis system with logistic source and non-sublinear production","authors":"Xiangdong Zhao,&nbsp;Jiao Wang","doi":"10.1016/j.aml.2025.109511","DOIUrl":"10.1016/j.aml.2025.109511","url":null,"abstract":"<div><div>This paper deals with a singular chemotaxis system with logistic source and non-sublinear production under homogeneous boundary condition: <span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mi>u</mi><mo>−</mo><mi>χ</mi><mo>∇</mo><mi>⋅</mi><mrow><mo>(</mo><mfrac><mrow><mi>u</mi></mrow><mrow><mi>v</mi></mrow></mfrac><mo>∇</mo><mi>v</mi><mo>)</mo></mrow><mo>+</mo><mi>r</mi><mi>u</mi><mo>−</mo><mi>μ</mi><msup><mrow><mi>u</mi></mrow><mrow><mi>k</mi></mrow></msup></mrow></math></span>, <span><math><mrow><msub><mrow><mi>v</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mi>v</mi><mo>−</mo><mi>v</mi><mo>+</mo><msup><mrow><mi>u</mi></mrow><mrow><mi>β</mi></mrow></msup></mrow></math></span> in a bounded convex domain <span><math><mrow><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></mrow></math></span> with <span><math><mrow><mi>n</mi><mo>≥</mo><mn>1</mn></mrow></math></span>, here <span><math><mrow><mi>χ</mi><mo>,</mo><mi>μ</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>, <span><math><mrow><mi>r</mi><mo>∈</mo><mi>R</mi></mrow></math></span>, <span><math><mrow><mi>k</mi><mo>&gt;</mo><mn>1</mn></mrow></math></span> and <span><math><mrow><mi>β</mi><mo>≥</mo><mn>1</mn></mrow></math></span>. It is proved that the system admits a global solution if <span><math><mrow><mi>k</mi><mo>&gt;</mo><mn>2</mn></mrow></math></span> with <span><math><mrow><mi>β</mi><mo>∈</mo><mrow><mo>[</mo><mn>1</mn><mo>,</mo><mi>k</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>, or <span><math><mrow><mi>k</mi><mo>&gt;</mo><mn>1</mn></mrow></math></span> and <span><math><mrow><mi>β</mi><mo>≥</mo><mn>1</mn></mrow></math></span> with <span><math><mrow><mi>χ</mi><mo>≤</mo><mfrac><mrow><mn>4</mn></mrow><mrow><mi>n</mi><msup><mrow><mi>β</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></mrow></math></span>. Moreover, the solution is globally bounded for the second case with <span><math><mrow><mi>r</mi><mo>≤</mo><mo>−</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>β</mi></mrow></mfrac></mrow></math></span>. This means that the logistic source along with non-sublinear production indeed benefits to ensure the global existence-boundedness of classical solution to this chemotaxis system with singular sensitivity.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"165 ","pages":"Article 109511"},"PeriodicalIF":2.9,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143511197","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}